The 25-year-old England international suffered a serious knee injury in last weekend's 2-2 draw at Manchester City and is now expected to be out for as long as nine months.
Welbeck only returned in February after a 10-month absence following an injury to his other knee - scoring a last-gasp winner against newly-crowned champions Leicester to mark his comeback.
Now Wenger, whose side host Aston Villa on the final day of the Barclays Premier League on Sunday, is concerned another spell on the sidelines could take its toll mentally on the former Manchester United man.
Asked if he was worried he would never see the old Welbeck again, Wenger replied: "There is no medical reason why he should not recover, but where there could be some psychological damage.
"It's huge commitment to get back to playing really freely.
"His play is explosive and committed so we need to make sure no tackles can hurt him when he comes back
But I don't think it is physically he will suffer."
Wenger intends to keep Welbeck away from the training ground in the early stages of his recovery - with his hopes of representing England at this summer's European Championships also dashed.
"The first stage when they are on crutches is the worst one," Wenger explained.
"In Danny's case I believe it will be 12 weeks on crutches without any support
Once the player can work again (and) he feels his recovery is going upwards, then you have done the job
But the first period is very depressing."
When asked how to combat the difficult period, the Gunners boss replied: "To get him out of here, as there is nothing worse than seeing everyone else jumping around and you cannot move.
"A training centre is not a hospital
They take care of people who are in a good shape
So the best is for them to be with people who are in similar situations.
"Different players react differently
I had the experience with Abou Diaby who when he came back to his first training season after a year out, we had to keep telling him to be cautious.
"Then we have had others with longer-term damage in their heads.
"What you avoid is the specific position in which you have been injured
Players are completely normally committed until they get into that position
Then it flashes up like an alert and the brain tells them 'Don't do that'."
While Welbeck is out, Wenger could hand Jack Wilshere his first start since a 4-1 win over West Brom nearly a year ago.
The 24-year-old has been eased back in following a broken leg but is ready from the off against Villa as he looks to prove his fitness to England boss Roy Hodgson before Monday's squad announcement.
Midfield trio Mikel Arteta, Mathieu Flamini and Tomas Rosicky are also likely to play some part after Wenger all but confirmed they would leave the club when their contracts expire next month.
Source : PA
Source: PA